"Drop Over" a higher channel in Video Sequence Editor
Where is only 3 channels needed to make unlimited count of fades. Use Cross or Gamma Cross for creating fade effect:

 

And you don't need to use keyframes in this case, fade effect will be from start of one strip to end from other strip.



And channel position doesn't matter, first and second strip sets up not by top and bottom order, but by selection: first and second selected.